A plot trope that involves a fantastic version of the most basic conflicts: Man vs. Beast.
In a Worldnote usually withoutThe Masquerade where humanity is terrorized by a race of Nigh Invulnerablebehemoths. Humanity is at a disadvantage, but at some point, they discover their enemies' weakness, and now have a fighting chance. And thus begins the tale of their struggle.
The most basic form of this is that a certain organization is in charge of recruiting people and equipping them with a specific set of equipment and/or skills vital to exploiting the weaknesses of the monsters they are fighting. In cases where there is a Masquerade, their purpose is to uphold it by preventing muggles from discovering the existence of such monsters.
The organization is usually the only one of its kind, but within a global reach there will often be "branches." Size and scope also vary. They can be as large and publicized as the military, but an Oddly Small Organization or a small The Squad/Five-Man Band would also do.
There usually isn't a prerequisite for its recruits; as long as they can fight, they can join. In verses that rely on Applied Phlebotinum, compatibilty with the phlebotinum is the only requirement, and you usually cannot refuse to join them, especially if compatible people are rare.
The monsters are usually characterized by being non-sentient beasts that devour or destroy humans or resources which make them a direct threat. Sometimes though, they are sentient but Always Chaotic Evil with little regard for self-preservation. Whatever their flavor, they're out to multiply and destroy, and our heroes' job is to stop them from doing so.
The monster's origin usually vary from being simply Aliens (or Angels & Demons or Robots & Golems); to coming from a single Hellgate; to being a result of Creating LifeGone Horribly Wrong; to being a mutant strain of an existing lifeform ; or a beastly sort of Henchmen Race created by the Big Bad; to simply just popping outof nowhere. Whatever their origin. There will already be quite a lot of them already by the time the story kicks in.
Whatever their origin, they will always be Nigh Invulnerable (or just Made of Iron) or have Healing Factor which makes them hard to kill. This doesn't mean they are invincible though. These monsters usually have an Achilles' Heel — usually in the form of Applied Phlebotinum that is the only thing that can harm them (which our organization would exploit as weapons), or a certain weak point in their body, which is usually a core placed in a strategic part of its body.
This trope has two common variations:
There must be an organization, or at the very least a team. Solo examples count if they have a group backing them, or at least, it is implied they have offscreen members.
The monsters must be impersonal "forces of nature" — as in, like the Generic Doomsday Villain, they are largely defined by the threat they pose rather than their motivations. Ones with sentient higher ups or ones with a bunch of sentient monsters of the same kind still count.
The monsters may or may not have a weakness. Their having a single origin or kind is more important than them having a weakness, whether Weaponized Weakness or Achilles' Heel.
Neon Genesis Evangelion: NERV is an organization that uses EVAs to fight an alien race known as the Angels. The reason Angels can't be destroyed by conventional weapons is because they sport AT-fields, Deflector Shields that can completely block even the explosive power of a multi-megaton bomb. The most efficent way to penetrate the AT-field is stated to be via close combat, for which the EVAs use high-frequency vibrating "Progressive Knives". The EVAs can even build up an AT-field of their own, and eventually it's revealed that the EVAs are actually created by cloning them from the same source the Angels themselves were born. The troops themselves are just three "Children" (which is also singular in-universe), who are the only ones capable of piloting said mecha... and they have issues to take care about themselves.
In the anime version of Soul Eater, the DWMA was founded to train Meisters and Weapons (who power up by eating souls) to hunt "Demon Eggs" (humans who have become corrupted by consuming the souls of the innocent), Kishin (Eldritch Abominations that form from said humans when they get too powerful) and their strongest, Kishin Asura, as well as Witches (from whom the weapons originally got their abilities). This trope didn't strictly apply to the manga, as it had no concept of Demon Eggs, and the DWMA hunted anyone Lord Death told them to. Many of them just happened to be very inhuman looking.
Gaist Crusher is a very simplistic take on this. Humanity has harvested powerful minerals called Gaimetals, but an alien threat seems to be turning them into violent monsters called Gaist. In order to combat them, the government has established the Gaist Crushers, humans using Powered Armor made of Gaimetal to fight. They're all very young for some reason, and the main character gets recruited after being forced to don Gaist Crusher gear in an emergency situation.
The Sky Girls are Japan's main line of defense against the setting's remaining WORMs ( Weapon Of Raid Machines). They are Older Than They Look girls chosen for their compatibility to the available Sonic Divers — which are Transforming Mecha with plane and bipedal modes. Ideal for high speed travel and aerial combat. The WORMs are artificial lifeforms consisting of millions of nanocells that take the forms of creatures they see. The girls are required to wear Latex Space Suit made of nanocells for protection because of this.
World Trigger features the Border Defense Agency against the aliens called Neighbors, who's members use the aliens' own Trion energy powered weapons called Trigger. Their members are people who have high trion levels. The BDA was formed specifically to defend against the neighbors. Although it was revealed in the first episode that what they were fighting were actually just their drones called Trion Soldiers and that the neighbors are actually Humanoid Aliens.
Seraph of the End: Vampire Reign: Earth's population is decimated by a virus, and the survivors are attacked by monsters or enslaved by vampires. Elite members of the army are able to make contracts with demons to earn phlebotinum weapons which are the only things capable of killing vampires.
Bleach': The Gotei 13 portrays itself as an organisation whose duty it is to protect humanity from the threat of hollows, human souls that have turned evil due Unfinished Business literally eating out the heart of their soul. However, the Shinigami were originally Balancers, monitoring the flow of souls between the World of the Living and the Soul Society. At some point they fell from their original purpose and became hollow-hunters, although they do retain at least one of their original abilities in the form of Soul Burial. Despite their current path, only the low-ranked Shinigami engage in hollow-hunting to obtain the experience necessary for dealing with threats to the Shinigami rather than to humanity. They therefore struggle to combat the threat to humanity, resulting in humans with power of their own to band together to produce the Quincies (the "Destroyers") to protect humans from hollows where Shinigami couldn't. Unfortunately, their method of fighting threatens the Balance of the World. As a result, the Quincies and Shinigami are at war with each other, benefiting no-one.
The titular warriors in Claymore are genetically engineered female supersoldiers designed to fight demons known as "yoma" and their evolved forms, giant monsters called Awakened Beings. The procedure to become a Claymore gives the user enhanced strength, speed, and abilities, but at great cost. This all turns out to be a front, as the Organization is actually breeding monsters in order to fight dragons.
In InuYasha, there used to be a group of people dedicated to exterminate the Youkai who were causing mayhem in the villages. During a gory attack orchestrated by Naraku, all of them except two were killed. The two survivors are Sango and her brother Kohaku.
One, the spirits are sentient and can be reasoned with. they can also have their powers sealed, reducing them into normal humans. so there really isn't much reason fighting them (unless they're psychos).
Two, the AST has their rival organization: Ratatorsk, who decided to have someone date these spirits to submission, since they conveniently all happen to be girls. This is because their leader is also sort of one, and had her powers sealed as well.
From Nobunagun, there is DOGOO, an organization formed specifically fight against aliens designated as Evolutionary Invasion Objects. They fight these with super powered individuals who are the genetic reincarnations of famous historical individuals.
Blue Exorcist features the Order of the True Cross, a worldwide organization dedicated to hunting down and exorcising demons that prey on humans. They're mostly content to leave the peaceful ones alone; some members even rely on them to fight.
In the The Matrix and Supernatural crossover fanfic Hunting Series the hunters are actually a group of loosely organized rebels around the Matrix's version of the world that delete 'supernatural' programs that kill innocent people. Examples of smaller teams are: Sam/Jessica and formerly the team of John Winchester and Bobby Singer.
Pacific Rim: Giant, city-destroying monsters (actually called "Kaiju" in-universe) emerge from a portal on the floor of the Pacific Ocean. The governments of the world realize that these Kaiju aren't going to stop coming, and that conventional weapons aren't suited to kill them without massive collateral damage. So the Jaeger program—consisting of Humongous Mecha, each piloted by two brain-linked humans—is created to deal with the threat.
In The Matrix Reloaded and The Matrix Revolutions, the Machines' main force for hunting humans in the real world are Sentinels, killer robots resembling cephalopods. In the human city of Zion, Captian Mifune leads a defense force of Armored Personnel Units, capable of dual-wielding guns big enough to take down the Sentinels. (Humans working outside can use EMP's to defend themselves from Sentinels, but for a variety of reasons, those are not practical to use anywhere near Zion.) This becomes a major plot point in Revolutions, when an army of Sentinels invades Zion, and Captain Mifune's team is the main line of defense.
John Carpenter's Vampires involves a group of vampire hunters out to stop the head vampire from getting a cross which will let him go out in the sun. There are other vampire hunting teams all around the world, all funded by the Catholic church.
Monsters vs. Aliens: General Monger leads a covert ops team that captures monsters and confines them in a secret base to keep the populace safe. Later, the monsters themselves become one such team, sent to battle an Alien Invasion.
Played with in the Night's Watch from A Song of Ice and Fire. They were created specifically to defend the realm from magical ice fearies called the Others (and their minions, the wights) but lack any specialized weaponry, and, by the time the series begins, the organization has devolved into an Army of Thieves and Whores after centuries of peace. Although as the series goes on, they may be played straight, as the Others are hinted to be making a comeback, and dragonglass is discovered to be very effective in fighting them.
The eponymous witchers in The Witcher series hunt all kinds of monsters, but specifically those who invaded the world after the Conjunction of the Spheres. They would fall under the phlebotinum-powered subtype, since they are genetically enhanced since childhood and have number of supernatural traits to complement their Training from Hell.
The Lakewalkers in Bujold's Sharing Knife series. They exist to hunt and kill Malices (Blight Boggles).
Live Action Television
In Supernatural, there is a loose organization of hunters, with Bobby serving as mission control, and later we learn about the Men of Letters.
Monster Hunter is based on this trope. In the games, an organization of hunters known as The Guild hires people so they can find and kill (or capture, depending on the case) large monsters. From a meta perspective, the hunters hired are the players who connect online and play together to complete the hunting quests.
Toukiden is another monster hunting game with a similar premise. Set in the land of Nakatsu. Your character is a Mononofu, One of the Warriors who specialize in fighting Oni. You and several other Mononofu live in and protect the village of Utakata from Oni attacks. Mononofu are armed with conventional weapons like Kusarigama, Bows, Longswords, and Gauntlets, but they also able to channel Mitamas— spirits of Ancient Warriors, to augment their abilities and attacks.
The main game also has the Vigilants of Stendarr, a militant order of priesthood that dedicate themselves to hunting daedra, witches, werewolves and the like.
In the Dragon Age series, the Grey Wardens' mission is to fight the darkspawn. In particular, Wardens are key to ending Blights (when the darkspawn corrupt an Old God into an Archdemon and attack the surface of Thedas); they are the only ones capable of killing Archdemons.
Nobodies, introduced in Kingdom Hearts II, who are born when a Heart is swallowed by darkness and becomes a Heartless. They are the remaining parts left behind by the heart: the body, giving a Nobody form, and the soul, giving the Nobody life.
Dream Eaters, who are a species of creature introduced in Kingdom Hearts 3D [Dream Drop Distance]. As their name suggests, they consume dreams. They fall under two major categories, Nightmares , which eat good dreams and plant bad ones, and Spirits, which eat bad dreams.
The main casts of Persona 3 and 4 consist of groups of teenagers (with some exceptions) who can summon Personas, which is necessary to defeatShadows. However, while 4's Investigation Team mainly kills shadows in the course of rescue operations, SEES was specifically formed to hunt down Shadows and keep them from attacking people. Mitsuru Kirijo, a former member of SEES, would later form the Shadow Operatives to deal with Shadows on a global scale.
The extinct-animal expanded versions of Zoo Tycoon give you the option of adding a Dino Capture Team to your zoo, whose team members round up and tranquilize dinosaurs that escape their exhibits and go on property-destruction rampages.
The students of Signal and Beacon (and others) use Mix And Match Weapons to fight The Grim. The Grim are a bunch of monstrous bigblack animals with something resembling a White Mask of Doom. They lack Aura and are more vulnerable to the weapons (which is good since they're Always Chaotic Evil and these weapons are in the good guys hands). The weapons used are amalgamations of a Melee weapon and a firearmException Jaune Arc's sword and collapsible shield the only things these weapons have in common are that they are powered by Dust. In addition to this, they and every other living being (except for Grim) have an aura which is used (either consciously or subconsciously) to augment their offensive and defensive capabilities.
D.I.A.P.P., the Division for the Investigation and Appropriation of Paranormal Phenomena from Angel Of Death is a division of the US government who, among other things, work to combat the numerous liches who go about devouring human souls.